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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectrally determined growth is generic


Author: Michael Renardy
Journal: Proc. Amer. Math. Soc. 124 (1996), 2451-2453
MSC (1991): Primary 47D06
MathSciNet review: 1328372
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Abstract: Let $A$ be the infinitesimal generator of a $C_0$-semigroup of operators in a Hilbert space. We consider the class of operators $A+B$, where $B$ is bounded. It is proved that the spectrum of $A+B$ determines the growth of the associated semigroup for ``most" operators $B$ (in the sense of Baire category).


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Additional Information

Michael Renardy
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: renardym@math.vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03417-X
PII: S 0002-9939(96)03417-X
Keywords: Linear stability, semigroups of operators
Received by editor(s): January 9, 1995
Received by editor(s) in revised form: February 23, 1995
Additional Notes: This research was supported by the National Science Foundation under Grant DMS–9306635 and by the Office of Naval Research under Grant N00014–92–J–1664.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society